17/3d-5=12+3d

Solution for 17/3d-5=12+3d equation:

17/3d-5=12+3d

We move all terms to the left:

17/3d-5-(12+3d)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R


We add all the numbers together, and all the variables

17/3d-(3d+12)-5=0

We get rid of parentheses

17/3d-3d-12-5=0

We multiply all the terms by the denominator


-3d*3d-12*3d-5*3d+17=0

Wy multiply elements

-9d^2-36d-15d+17=0

We add all the numbers together, and all the variables

-9d^2-51d+17=0

a = -9; b = -51; c = +17;
Δ = b2-4ac
Δ = -512-4·(-9)·17
Δ = 3213
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3213}=\sqrt{9*357}=\sqrt{9}*\sqrt{357}=3\sqrt{357}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{357}}{2*-9}=\frac{51-3\sqrt{357}}{-18}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{357}}{2*-9}=\frac{51+3\sqrt{357}}{-18}
$